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Source: Indonesia MO 2022/6

October 5, 2022

geometry

Problem Statement

In a triangle

ABC

,

D

and

E

lies on

AB

and

AC

such that

DE

is parallel to

BC

. There exists point

P

in the interior of

BDEC

such that

\angle BPD = \angle CPE = 90^{\circ}

Prove that the line

AP

passes through the circumcenter of triangles

EPD

and

BPC

.

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